The spectrum of the growth rate of the tunnel number is infinite-Reference-Cited by-同舟云学术

The spectrum of the growth rate of the tunnel number is infinite

Published:2016-02-02 Issue:8 Volume:144 Page:3609-3618
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Baker Kenneth,Kobayashi Tsuyoshi,Rieck Yo’av

Abstract

For any ϵ > 0 \epsilon > 0 we construct a hyperbolic knot K ⊂ S 3 K \subset S^{3} for which 1 − ϵ > g r t ( K ) > 1 1 - \epsilon > \mathrm {gr}_t(K) > 1 . This shows that the spectrum of the growth rate of the tunnel number is infinite.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2016-144-08/S0002-9939-2016-12957-2/S0002-9939-2016-12957-2.pdf

Reference18 articles.

1. K. L. Baker and K. Motegi, Twist families of L-space knots, their genera, and Seifert surgeries, available at http://arxiv.org/abs/1506.04455., June 2015.

2. Kenneth L. Baker, Closed essential surfaces in the complements of large volume Berge knots, available at http://arxiv.org/abs/math/0509082v1.

3. Surgery descriptions and volumes of Berge knots. I. Large volume Berge knots;Baker, Kenneth L.;J. Knot Theory Ramifications,2008

4. Kenneth L. Baker, Cameron Gordon, and John Luecke, Bridge number and integral Dehn surgery, Version 1, available at http://arxiv.org/abs/1303.7018v1, to appear in Algebr. Geom. Topol.

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